Sorry to hear about the cut on your face! This is a great question, and there are indeed several things that you can do to keep down the scarring as the cut heals.
First of all, it is very important that you don't pick at the scar or at the scab. The area must be left to heal on its own, and any manipulation of the area with your hands raises the chance that the area will get infected or bleed, both of which will raise the chances of a larger scar.
Another thing you can do is cover the cut with a thin layer of an occlusive ointment, like antibacterial ointment or vaseline. What this does is keep the air out and allow the new skin cells to grow into the cut smoothly and quickly.
When the cut does heal finally, you may have a small discolored area of new skin. However, as long as you keep this well moisturized with a good facial lotion and avoid sun damage (wear sun screen) the color should fade slowly over a few weeks to months.
I recommend that you talk to your primary care doctor
or a dermatologist
to get this process moving forward correctly, and to make sure there aren't additional complications.